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@SteamTrain @SForrestLO 

Appreciate your suggestions. I think it's confirmed that the problem lies with TT's desktop product, as I received this email from TT:

 

We’re reaching out because some of our TurboTax Desktop customers who’ve successfully filed their tax returns are seeing a message in-product that says their e-file isn’t complete. This message is popping up due to an issue in our desktop product that we’re actively working to fix.

We can confirm that your tax return has been filed and accepted. Please disregard the message in your desktop product that says your return has not yet been filed.

No action is needed on your end. We’ll follow-up with another email once the issue has been resolved, at which point TurboTax will reflect your filing status as successful.

 

I suppose that's why the TT support person I spoke with recommended that I file an amended Federal return as a work-around to be able to e-file my State return. Much as I hate paper, I think I'll have to print and mail my State return as I don't know how long it will take TT to fix this glitch.